where \(\epsilon ^\ast _{i}\)  is given by Eq. (REF ) with
replacing
\(n_i\)  by \(n_i^\ast \) .
These expressions are similar to those of
Eq. (REF ) at the first order in \(\epsilon _i\) .
We proved that at small \(\epsilon ^\ast _i\) 
the expansion of the pressure
over powers of \(\epsilon ^\ast _i\) 
becomes rapidly convergent
to the exact results, and a few first
terms give already a good approximation.
Our Eq. (REF ),
in contrast to Eq. (REF )
discussed in Refs. [1]}, [2]},
takes into account the particle interaction effects
(cf. with the previous section ).
A new point of
our consideration is the analytical estimates
of the QS effects
in a mixed system of
interacting fermions and bosons.
Similarly to the ideal gases, the quantum corrections in
Eq. (REF ) increases
with the particle number density \(n_i\)  and decreases with the system
temperature \(T\) ,
particle mass \(m_i\) , and degeneracy factor \(g_i\) .
